1209.2968 (Jeffrey Galkowski)

Quantum Ergodicity for a Class of Mixed Systems    [PDF]

Jeffrey Galkowski

We consider sets of quasimodes for the Dirichlet Laplacian on a domain with boundary where the geodesic flow exhibits mixed dynamical behavior. We assume that the billiard flow has an invariant ergodic component, U, and study defect measures, \mu, of positive density sequences of almost orthogonal quasimodes. We demonstrate that, when restricted to U, \mu=c\mu_L where \mu_L is the Liouville measure. In order to do this, we adapt quantum ergodicity results to the case of quasimodes. Finally, using Bunimovich's mushroom billiards, we give an example where our results apply.

View original: http://arxiv.org/abs/1209.2968